Definitely dont wash the eggs. Mites cant harm the eggs, plus eggs are porous and it is very easy to introduce contaminants through the shell. As close as the eggs are to hatching, they should be disturbed as little as possible.
The broody definitely needs to be treated for the mites asap. Permethryn is safe and effective for both adults and chicks. I dust it directly on the hen, but not directly on young chicks. I also dust the ground of their living area. The chicks will be "dusted" by sleeping under the hen, as well as climbing through her feathers. They will also be dusted when they bathe in the permethryn treated dirt. The main thing is to get the mites off the hen before the eggs hatch, so the chicks dont get mites in the first place.
What material are you using in the nesting box? Hay and straw give mites a place to thrive. Shavings is much less mite-friendly. You will need to transfer the eggs to a new mite-free nest box, or remove the eggs while you treat the box she is currently in. She may come off the eggs if you move her. But hopefully not this late in incubation, since she can likely already feel the eggs moving & is also communicating with them by sound. If you feel moving her to a new broody hotel is best, well u gotta do what u gotta do.
Before you move the eggs, pay close attention to the position they are in under the hen. At 19 days, they are essentially in "lockdown", same as if they were in an artficial incubator. The artificial incubator stops turning the eggs on day 18; the hen does the same.
Remove the eggs from the infested nestbox, placing them in the exact same position into a new clean nestbox, or into a temporary nestbox while you treat the infested one. If an egg rolls out of its former position dont worry. Yes the chick will need to rotate into hatching position again, which can sap strength, but not nearly as much as hatching into a mite-infested environment.
Good luck and please update. I hope you kill all the mites & the hatch goes smoothly.